Subtraction techniques are used to distinguish moving objects or foregrounds that are being tracked from a static background. To prevent possible local misclassifications, the subspace spanned by low-rank features computed from a multilinear singular value decomposition (MLSVD), can be used to filter out noises or gradual changes from the background. However, as it is prohibitively expensive to compute a new MLSVD from scratch at every iteration, we propose an adaptive and efficient method for updating an MLSVD by reusing previous decompositions while tracking more accurate decomposition errors. The experimental results reveal that the proposed MLSVD update algorithm exhibits a faster execution speed and better accuracy than other MLSVD update algorithms used in background subtraction applications.